Finite Group Databasebeta

← #25253445

Subgroups — #25253445

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146963C211yesmaximal, characteristic, complemented
2#19146283C211yesmaximal, characteristic
3#19136825C211yesmaximal, characteristic, complemented
4#19136794C211yesmaximal, characteristic, complemented
5#19136755C211yesmaximal, characteristic, complemented
6#19136689C211yesmaximal, characteristic, complemented
7#19136687C211yesmaximal, characteristic, complemented
8#19136656C211yesmaximal, characteristic, complemented
9#19136537C211yesmaximal, characteristic, complemented
10#19136525C211yesmaximal, characteristic, complemented
11#19136446C211yesmaximal, characteristic, complemented
12(C22⋊D43)⋊C16C211yesmaximal, characteristic, complemented
13#19136300C211yesmaximal, characteristic, complemented
14#357×D43C211yesmaximal, characteristic, complemented
15C43×#2234C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18#14583588—21no—
19#14583546—21no—
20C2×Dic344C2211yescharacteristic, complemented
21C2×#13063270C2211yescharacteristic
22C2×#13063269C2211yescharacteristic
23C22×C43⋊C16C2211yescharacteristic, complemented
24C2×C16×D43C2211yescharacteristic
25#14583300C2211yescharacteristic, complemented
26#14583282C2211yescharacteristic
27#14583240—21no—
28#14583231—21no—
29#14583209—21no—
30#14583141C2211yescharacteristic
31#14583141C2211yescharacteristic
32#14583140C2211yescharacteristic, complemented
33#14583113—21no—
34#14583051—21no—
35#14583042—21no—
36#14582993C2211yescharacteristic, complemented
37#14582981C2211yescharacteristic
38C8×C22⋊D43C2211yescharacteristic
39#107×D43C2211yescharacteristic
40#14582726C2211yescharacteristic, complemented
41Dic43⋊C16C2211yescharacteristic, complemented
42#14582704C2211yescharacteristic, complemented
43#14582702C2211yescharacteristic, complemented
44#14582702C2211yescharacteristic, complemented
45#14582702C2211yescharacteristic, complemented
46#14582701C2211yescharacteristic
47#14582700C2211yescharacteristic
48#14582699C2211yescharacteristic
49#14582699C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51C16×Dic43C2211yescharacteristic, complemented
52C43×#466C2211yescharacteristic
53C43×#427C2211yescharacteristic, complemented
54C43×#367C2211yescharacteristic, complemented
55C43×#366C2211yescharacteristic, complemented
56C43×#357C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×C22⋊C16C2211yescharacteristic, complemented
59C2×#10621898—21no—
60C2×D4×D43—21no—
61#13063347—22no—
62#13063347—41no—
63C2×Dic172C2311yescharacteristic
64C2×Dic172C2311yescharacteristic
65C2×#10621873—21no—
66C2×#10621883—21no—
67C2×D344C2311yescharacteristic
68C2×#10621882—21no—
69D8×D43—22no—
70D8×D43—41no—
71C2×C8×D43C2311yescharacteristic
72#13063318—41no—
73#13063317—41no—
74#13063316—21no—
75#13063312—21no—
76#13063307—41no—
77#13063307—41no—
78#13063305—21no—
79#13063305—21no—
80#13063304—21no—
81#13063296—41no—
82#13063293—41no—
83#13063290—21no—
84#13063287—21no—
85C4×C22⋊D43D411yescharacteristic
86#13063282—41no—
87C4⋊C4×D43—21no—
88C22⋊C4×D43—41no—
89Dic344—41no—
90#13063270—22no—
91#13063269—41no—
92C2×C43⋊C16—41no—
93C2×C43⋊C16C2311yescharacteristic
94C2×C43⋊C16C2311yescharacteristic
95C16×D43—41no—
96#13063259C2311yescharacteristic
97#13063258—21no—
98#13063256—21no—
99Dic43⋊C8D411yescharacteristic
100#13063250—21no—
101#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063245—21no—
105C22⋊(C43⋊C8)D411yescharacteristic
106(C2×D43)⋊C8D411yescharacteristic
107C8×Dic43C2311yescharacteristic
108C2×D8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110#121×C43—21no—
111#117×C43—21no—
112C2×C16×C43C2311yescharacteristic
113C2×C16×C43C2311yescharacteristic
114#107×C43C2311yescharacteristic
115#107×C43C2311yescharacteristic
116#107×C43C2311yescharacteristic
117#106×C43—21no—
118#102×C43—21no—
119C23×D43—41no—
120C2×D4×C43—21no—
121C2×D4×C43—41no—
122C22×C4×C43C2×D411yescharacteristic
123C2×C22⋊D43—41no—
124C2×C22⋊D43—41no—
125C2×C22⋊D43D811yescharacteristic
126D4×D43—42no—
127D4×D43—81no—
128#10621898—42no—
129#10621898—81no—
130C2×D172—21no—
131C2×C4×D43—41no—
132C2×C4×D43—41no—
133C2×C4×D43—41no—
134C2×C4×D43C2×D411yescharacteristic
135C2×Dic86—21no—
136C2×Dic86—21no—
137D8×C43—21no—
138D8×C43—21no—
139C2×C8×C43—21no—
140C2×C8×C43—21no—
141C2×C8×C43C2×D411yescharacteristic
142C2×C8×C43C2411yescharacteristic
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C22⋊C4×C43—41no—
147C22⋊C4×C43—41no—
148C42×C43—41no—
149C22⋊Dic43—41no—
150C22⋊Dic43—41no—
151C22⋊Dic43—41no—
152C22⋊Dic43D811yescharacteristic
153#10621883—81no—
154#10621882—42no—
155(C2×D43)⋊C4—41no—
156(C2×D43)⋊C4—41no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4D811yescharacteristic
159C4⋊Dic43—21no—
160C4⋊Dic43—41no—
161C4⋊Dic43—41no—
162C4⋊Dic43—41no—
163Dic43⋊C4—41no—
164Dic43⋊C4—41no—
165Dic43⋊C4—41no—
166Dic43⋊C4—41no—
167Dic43⋊C4D811yescharacteristic
168C4×Dic43—41no—
169C4×Dic43C2×D411yescharacteristic
170C2×C43⋊C8C2×D411yescharacteristic
171C2×C43⋊C8C2×D411yescharacteristic
172Dic172—21no—
173Dic172—21no—
174Dic172—21no—
175Dic172—21no—
176D344—21no—
177D344#4112yes—
178#10621873—42no—
179C8×D43—21no—
180C8×D43—21no—
181C16×C43—21no—
182C16×C43—21no—
183C43⋊C16—21no—
184C43⋊C16—21no—
185C23×C43—41no—
186C23×C43C2×D811yescharacteristic
187C22×D43—41no—
188C22×D43—82no—
189C22×D43—82no—
190C22×D43—161no—
191C22×D43C2×D811yescharacteristic
192D4×C43—41no—
193D4×C43—41no—
194D4×C43—161no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43C2×D811yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C22⋊D43—22no—
203C22⋊D43—82no—
204C22⋊D43—82no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43C2×D811yescharacteristic
209C2×Dic43C2×D811yescharacteristic
210C2×Dic43C2×D811yescharacteristic
211D172—22no—
212D172—41no—
213C4×D43—21no—
214C4×D43—21no—
215C4×D43—82no—
216C4×D43—82no—
217C4×D43—161no—
218Dic86—41no—
219Dic86—41no—
220Dic86—41no—
221Dic86—41no—
222C8×C43—21no—
223C8×C43C2×#4111yescharacteristic
224C8×C43H(5,𝔽2)11yescharacteristic
225C43⋊C8—21no—
226C43⋊C8—21no—
227#33863—431nomaximal, Sylow
228C22×C43—21no—
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—81no—
232C22×C43—81no—
233C22×C43—81no—
234C22×C43C22×D811yescharacteristic
235C2×D43—21no—
236C2×D43—21no—
237C2×D43—42no—
238C2×D43—81no—
239C2×D43—81no—
240C2×D43—164no—
241C2×D43#50812yes—
242C4×C43—21no—
243C4×C43—81no—
244C4×C43—81no—
245C4×C43—81no—
246C4×C43#54611yescharacteristic
247C4×C43#57711yescharacteristic
248Dic43—21no—
249Dic43—21no—
250Dic43—21no—
251Dic43—81no—
252Dic43—81no—
253Dic43—81no—
254#3336—431no—
255#3280—431no—
256#2242—431no—
257#2235—431no—
258#2234D4311yescharacteristic, complemented
259#2228—431no—
260#2217—431no—
261#2216—431no—
262#2211—431no—
263#2189—431no—
264#2187—431no—
265C4×SD32—431no—
266D4×C16—431no—
267#2138—431no—
268C2×#357—431no—
269C2×C43—41no—
270C2×C43—161no—
271C2×C43#329411yescharacteristic
272C2×C43C2×#50811yescharacteristic
273C2×C43#341611yescharacteristic
274D43—22no—
275D43—82no—
276C2×#135—431no—
277C22×D8—431no—
278#552—861no—
279#546—861no—
280C2×Q32—431no—
281C2×SD32—431no—
282C2×SD32—431no—
283C22×C16—431no—
284C22×C16—431no—
285#499—431no—
286#495—431no—
287#485—861no—
288#483—861no—
289#479—861no—
290#467—431no—
291#467—431no—
292#467—431no—
293#466C2×D4311yescharacteristic
294#463—861no—
295#450—861no—
296#449—861no—
297C4×Q16—431no—
298C4×D8—431no—
299C8×D4—431no—
300#427C2×D4311yescharacteristic, complemented
301C2×#107—431no—
302#367—431no—
303#367C2×D4311yescharacteristic, complemented
304#366C2×D4311yescharacteristic, complemented
305C4⋊C16—431no—
306#358—431no—
307#358—431no—
308#358—431no—
309#358—431no—
310#357—431no—
311#357—431no—
312#357—431no—
313#357—431no—
314#357C2×D4311yescharacteristic
315#357C2×D4311yescharacteristic
316C22⋊C16—431no—
317C22⋊C16C2×D4311yescharacteristic, complemented
318C4×C16—431no—
319C43#3386311yescharacteristic, complemented, Sylow
320C2×#41—861no—
321C22×D4—861no—
322#135—862no—
323#135—1721no—
324C2×Q16—431no—
325C2×Q16—431no—
326C2×SD16—861no—
327C2×SD16—861no—
328C2×D8—431no—
329C2×D8—861no—
330C2×D8—862no—
331C2×D8—1721no—
332C2×D8C22×D4311yescharacteristic
333C22×C8—431no—
334C22×C8C22×D4311yescharacteristic
335#126—1721no—
336#125—861no—
337#125—1721no—
338#124—861no—
339#123—1721no—
340#123—1721no—
341C22⋊Q8—861no—
342C22⋊Q8—861no—
343C22⋊Q8—861no—
344#121—21no—
345#121—1721no—
346#120—1721no—
347C4×Q8—861no—
348C4×D4—431no—
349C4×D4—861no—
350#117—21no—
351#117—1721no—
352C2×C4⋊C4—861no—
353C2×C22⋊C4—1721no—
354Q32—1721no—
355SD32—862no—
356SD32—1721no—
357C2×C16—431no—
358C2×C16—431no—
359C2×C16—1721no—
360C2×C16—1721no—
361C2×C16C22×D4311yescharacteristic
362C2×C16C22×D4311yescharacteristic
363#107—431no—
364#107—861no—
365#107C22×D4311yescharacteristic
366#107C22×D4311yescharacteristic
367#107C22×D4311yescharacteristic
368#106—21no—
369#106—861no—
370C4⋊C8—431no—
371#103—861no—
372#103—861no—
373#103—861no—
374#103—861no—
375#102—21no—
376#102—861no—
377C22⋊C8—431no—
378C22⋊C8—431no—
379C4×C8—431no—
380C24—1721no—
381#41—3441no—
382#41—1722no—
383C2×Q8—861no—
384C2×Q8—861no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—431no—
388C2×D4—861no—
389C2×D4—3441no—
390C2×D4—1721no—
391C2×D4—1722no—
392C2×D4—1721no—
393C22×C4—431no—
394C22×C4—1721no—
395C22×C4—1721no—
396C22×C4—1721no—
397C22×C4D4×D4311yescharacteristic
398Q16—861no—
399Q16—861no—
400Q16—861no—
401Q16—861no—
402SD16—3441no—
403SD16—1722no—
404D8—21no—
405D8—21no—
406D8—432no—
407D8—861no—
408D8—1722no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—431no—
412C2×C8—431no—
413C2×C8—861no—
414C2×C8—861no—
415C2×C8D4×D4311yescharacteristic
416C2×C8C23×D4311yescharacteristic
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—431no—
421C4⋊C4—861no—
422C4⋊C4—1721no—
423C4⋊C4—1721no—
424C4⋊C4—1721no—
425C4⋊C4—1721no—
426C4⋊C4—1721no—
427C4⋊C4—1721no—
428C4⋊C4—1721no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—431no—
432C22⋊C4—431no—
433C22⋊C4—1721no—
434C22⋊C4—1721no—
435C22⋊C4—1721no—
436C22⋊C4—1721no—
437C22⋊C4—1721no—
438C22⋊C4—1721no—
439C42—41no—
440C42—431no—
441C42—1721no—
442C16—21no—
443C16—21no—
444C16—861no—
445C16—861no—
446C23—41no—
447C23—431no—
448C23—3442no—
449C23—3442no—
450C23—1721no—
451C23—6881no—
452C23D8×D4311yescharacteristic
453Q8—1721no—
454Q8—1721no—
455Q8—1721no—
456Q8—1721no—
457D4—41no—
458D4—41no—
459D4—161no—
460D4—862no—
461D4—862no—
462D4—3442no—
463D4—3442no—
464D4—1721no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—431no—
471C2×C4—431no—
472C2×C4—431no—
473C2×C4—861no—
474C2×C4—861no—
475C2×C4—3442no—
476C2×C4—3442no—
477C2×C4—1721no—
478C2×C4—1721no—
479C2×C4—1721no—
480C2×C4—6881no—
481C2×C4D8×D4311yescharacteristic
482C2×C4C2×D4×D4311yescharacteristic
483C8—21no—
484C8—861no—
485C8—861no—
486C8#41×D4311yescharacteristic
487C8#1306337111yescharacteristic
488C22—21no—
489C22—21no—
490C22—21no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—432no—
495C22—861no—
496C22—861no—
497C22—3441no—
498C22—3441no—
499C22—1722no—
500C22—6884no—
501C22C2×D8×D4311yescharacteristic
502C4—21no—
503C4—81no—
504C4—81no—
505C4—81no—
506C4—861no—
507C4—861no—
508C4—861no—
509C4—3441no—
510C4—3441no—
511C4—3441no—
512C4#1458354111yescharacteristic
513C4#1458370811yescharacteristic
514C2—41no—
515C2—161no—
516C2—862no—
517C2—3442no—
518C2#1914640611yescharacteristic
519C2#508×D4311yescharacteristic
520C2#1914774111yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2234C2
socleC22×C43C22×D8
prime radical#19146283C2
hypercenter#2234D43
hypocenterC43#33863
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19146963C2semidirect
3. #19136825C2semidirect
4. #19136794C2semidirect
5. #19136755C2semidirect
6. #19136689C2semidirect
7. #19136687C2semidirect
8. #19136656C2semidirect
9. #19136537C2semidirect
10. #19136525C2semidirect
11. #19136446C2semidirect
12. (C22⋊D43)⋊C16C2semidirect
13. #19136300C2semidirect
14. #357×D43C2semidirect
15. C43×#2234C2semidirect
20. C2×Dic344C22semidirect
23. C22×C43⋊C16C22semidirect
25. #14583300C22semidirect
32. #14583140C22semidirect
36. #14582993C22semidirect
40. #14582726C22semidirect
41. Dic43⋊C16C22semidirect
42. #14582704C22semidirect
43. #14582702C22semidirect
44. #14582702C22semidirect
45. #14582702C22semidirect
51. C16×Dic43C22semidirect
53. C43×#427C22semidirect
54. C43×#367C22semidirect
55. C43×#366C22semidirect
58. C43×C22⋊C16C22semidirect
258. #2234D43semidirect
300. #427C2×D43semidirect
303. #367C2×D43semidirect
304. #366C2×D43semidirect
317. C22⋊C16C2×D43semidirect
319. C43#33863semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191469632
#191462832
#191368252
#191367942
#191367552
#191366892
#191366872
#191366562
#191365372
#191365252
#191364462
(C22⋊D43)⋊C162
#191363002
#357×D432
C43×#22342
#3386343